Backward-to-forward jump rates on a tilted periodic substrate

In biased and soft-walled channels: Insights into transport phenomena and damped modulation

The motion of a particle along a channel of finite width is known to be affected by either the presence of energy barriers or changes in the bias forces along the channel direction. By using the lateral equilibrium hypothesis, we have successfully derived the effective diffusion coefficient for soft-walled channels, and the diffusion is found to be influenced by the curvature profile of the potential. A typical phenomenon of diffusion enhancement is observed under the appropriate parameter conditions. We first discovered an anomalous phenomenon of quasi-periodic enhancement of oscillations, which cannot be captured by the one-dimensional effective potential, under the combination of sub-Ohmic damping with two-dimensional restricted channels. We innovatively develop the effective potential and the formation mechanism of velocity variance under super-Ohmic and ballistic damping, and meanwhile, ergodicity is of concern. The theoretical framework of a ballistic system can be reinterpreted through the folding acceleration theory. This comprehensive analysis significantly enhances our understanding of diffusion processes in constrained geometries.

Transition of multidiffusive states in a biased periodic potential

We study a frequency-dependent damping model of hyperdiffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to ω^{δ-1} at low frequencies with 0<δ<1 (sub-Ohmic damping) or 1<δ<2 (super-Ohmic damping), where the frequency-dependent damping is deduced from the noise by means of the fluctuation-dissipation theorem. It is shown that for super-Ohmic damping and certain parameters, the diffusive process of the particle in a titled periodic potential undergos sequentially four time regimes: thermalization, hyperdiffusion, collapse, and asymptotical restoration. For analyzing transition phenomenon of multidiffusive states, we demonstrate that the first exist time of the particle escaping from the locked state into the running state abides by an exponential distribution. The concept of an equivalent velocity trap is introduced in the present model; moreover, reformation of ballistic diffusive system is also considered as a marginal situation but does not exhibit the collapsed state of diffusion.

Diffusion and mobility of anisotropic particles in tilted periodic structures

We numerically investigated the transport of anisotropic particles in tilted periodic structures. The diffusion and mobility of the particles demonstrate distinct behaviors dependence on the shape of the particles. In two-dimensional (2D) periodic potentials, we find that the mobility is influenced a little by the anisotropy of the particle, while the diffusion increases monotonically with the increasing of the particle anisotropy for large enough biased force. However, due to the sensitivity of the channels for the particle anisotropy, the transport in smooth channels is obviously different from that in energy potentials. The mobility decreases monotonically with the increasing of the particle anisotropy, while the diffusion can be a non-monotonic function of the particle anisotropy with a peak under appropriate biased force.

Relative stability of dynamical states and stochastic resonance in a sinusoidal potential

Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.

Fluctuation-induced drift in a gravitationally tilted optical lattice

Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the direction of the tilt. The magnitude of the drift varies with the ratio between the bias force and the trapping potential. This can be closely compared to a theoretical model system, based on a Fokker-Planck-equation formalism. We show that the level of control and measurement precision we have in our system, which is based on cold atoms trapped in a three-dimensional dissipative optical lattice, makes the experimental setup suitable as a testbed for fundamental statistical physics. We simulate the system with a very simplified and general classical model, as well as with an elaborate semiclassical Monte Carlo simulation. In both cases, we achieve good qualitative agreement with experimental data.

Transient chaos induces anomalous transport properties of an underdamped Brownian particle

For an underdamped Brownian particle in a one-dimensional periodic potential we theoretically predict three unusual transport properties: (i) A static bias force (of either sign) generates an average particle motion in the opposite direction. (ii) A small bias leads to a particle transport in the direction of the bias, but upon increasing the bias the particle velocity reverses direction. (iii) For a given bias force, the particle motion follows the direction of the force for low temperatures, but upon increasing the temperature reverses its direction. The considered model is shown to be minimal for the occurrence of these phenomena. A detailed analysis of its deterministic properties and the influence of thermal noise is carried out with numerical simulations that are complemented by analytical approximations. Intuitive explanations of the basic mechanism behind the three effects are provided; their origin is attributed to a subtle interplay between the stability of coexisting attractors, noise induced metastability, and transient chaos. An experimental system for the realization of the predicted effects is given within the Stewart-McCumber model for Josephson junctions. Suitable parameter values for which these effects can be observed are quite realistic experimentally.

Anomalous diffusion in periodic potentials under self-similar colored noise

We present numerical studies of anomalous diffusion in periodic potentials by simulating a generalized Langevin equation. It is proved that the particle driven by a thermal colored noise with the spectral density vanishing at zero frequency allows superdiffusive motion. It is found that the system subjected to sub- or superohmic damping exhibits two motion modes in a corrugated plane: running oscillated state and mixed running and oscillating states, respectively. Induced, the anomalous power can be enhanced up twice for the latter case and thus a wide range of diffusive regimes is observed with changing titled force.

Time-dependent barrier passage of a non-Ohmic damping system

We consider a particle passing over the saddle point of an inverse harmonic potential, which is described by a generalized Langevin equation with a non-Ohmic damping of power exponent delta. The time-dependent passing probability and transmission coefficient are obtained analytically by using the reaction flux method. It is shown that the overshooting phenomenon for the passing probability appears in the regime 0<delta<1 and the backflow recrossing over the saddle point is observed, where a nonmonotonous time dependence of the passage probability is detected. The long memory aspect of friction is at the origin of this behavior. Thus the steady transmission coefficient is also a nonmonotonous function of delta.

Transition from smooth sliding to stick-slip motion in a single frictional contact

We show that the transition from smooth sliding to stick-slip motion in a single planar frictional junction always takes place at an atomic-scale relative velocity of the substrates.

Noise-assisted transport on symmetric periodic substrates

The rectification of a massive Brownian particle moving on a periodic substrate can be achieved in the absence of spatial asymmetry, by having recourse to (at least) two periodic, zero-mean input signals. We determine the relevant drift current under diverse operation conditions, namely, additive and multiplicative couplings, adiabatic and fast oscillating drives, and propagating substrate modulations. Distinct rectification mechanisms result from the interplay of noise and commensuration of the input frequencies, mediated through the nonlinearity of the substrate. These mechanisms are then extended to characterize soliton transport along a directed multistable chain. As the side-wise soliton diffusion is ultimately responsible for the transverse diffusion of such chains, our approach provides a full account of the Brownian motion of both pointlike and linear objects on a periodic substrate.

Brownian motors: current fluctuations and rectification efficiency

With this work, we investigate an often neglected aspect of Brownian motor transport, namely, the role of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time-, and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, unidirectional motion of the Brownian motor with few back-turns only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.

Role of long jumps in surface diffusion

We analyze a probability of atomic jumps for more than one lattice spacing in activated surface diffusion. First, we studied a role of coupling between the x and y degrees of freedom for the diffusion in a two-dimensional substrate potential. Simulation results show that in the underdamped limit the average jump length <lambda> scales with the damping coefficient eta as <lambda> proportional, variant eta(-sigma(lambda)) with 1/2<or=sigma(lambda) less, similar 2/3, so that the diffusion coefficient behaves as D proportional, variant eta(-sigma) with 0<or=sigma less, similar 1/3. Second, we introduced a realistic friction coefficient for the phonon damping mechanism and developed the technique for Langevin equation with a velocity-dependent friction coefficient. The study of diffusion in this model shows that long jumps play an essential role for diffusing atoms of small masses, especially in two limiting cases, in the case of a large Debye frequency of the substrate, when the rate of phonon damping is low, and in the case of a small Debye frequency, when the one-phonon damping mechanism is ineffective.

Diffusion in tilted periodic potentials: Enhancement, universality, and scaling

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare (potential-free) thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

Role of entropy barriers for diffusion in the periodic potential

Diffusion of a particle in the N-dimensional external potential which is periodic in one dimension and unbounded in the other N-1 dimensions is investigated. We find an analytical expression for the overdamped diffusion and study numerically the cases of moderate and low damping. We show that in the underdamped limit, the multidimensional effects lead to a reduction (compared to the one-dimensional motion) in the jump lengths between subsequent trappings of the atom at the minima of the external periodic potential. As an application, we consider the diffusion of a dimer adsorbed on the crystal surface.